I have one like this, too. It was inspired by DIY inflation but I haven't used caulk or anything permanent (yet).

The nipples I'm using don't entirely match up, so there is a bit of gapping depending on which way/order I stack them (turned inside-out or not, too).

Since I didn't fill them, they can collapse which reduces the holding power (depending on how much skin is between them).

Anyway, up until this week I have just had a catheter stuck in the end and used a binder clip to hold pressure (inflating by using my mouth). It works well enough but not when dressed (clothing pushes the catheter a bit which allows leakage). But it is lightweight and simple.

I had been envisioning your method for some time and decided to try it out. At first, I tried a Presta valve since there isn't a spring to push against and the inside pressure creates the seal. Well, the pressure I can create isn't enough to get the valve to seal well so it leaks. I have a valve stem so I tried that and it's much better.

I found out that inside-out or not matters due to the swirl ridges against the valve stem.

I am using a Schrader ball chuck on a quick connect and a hose (part of a catheter (the larger end that goes on a bag—perfect fit) and some random hose I stretched over the catheter). Side note: I don't think the hose needs to be special (food grade), just anything clean enough that I'm willing to put in my mouth. You can buy various size hoses by the foot at hardware stores.

Since I don't have caulk to support the nipple, it's easily deformed. When I put the ball chuck on, it needs pressure to both open the seal in it and push down the spring in the Schrader valve. I can't firmly hold the assembly because then there isn't a seal. Holding the valve stem is really difficult (normally, there is a tire/rim for resistance).

The ball chuck is heavier than I realized and with the hose, it's a fair bit to have in a pocket.

What do you recommend?